-12 -4 8. (4 pts) Let ū1 = -12 and U2 = -15 These vectors form a basis for a subspace -6 -11 V of R3. Starting with 71, 72, use the Gram-Schmidt process to find an orthonormal basis ū1, ū2 for V. -
(2 points) Let 4- -1 01 1 1-1 0-2]. Find orthonormal bases of the kernel, row space, and image (column space) of A (b) Basis of the row space: (c) Basis of the image (column space)
Will rate once all is completed. 1) 2) 3) 4) (12 points) Find a basis of the subspace of R that consists of all vectors perpendicular to both El- 1 1 0 and 7 Basis: , then you would enter [1,2,3],[1,1,1] into the answer To enter a basis into WeBWork, place the entries. each vector inside of brackets, and enter a list these vectors, separated by commas. For instance if vour basis is 31 2 and u (12 points) Let...
-4 0 -1 1 1 2 7 6 (1 pt) Let A 1 5 -3 -1 3 13 -1 -1 Find orthogonal bases of the kernel and image of A 10 -1 1 2 Basis of the kernel: -1 1 -1 3 -3 1 8 Basis of the image: -1 1 -1 7 (1 pt) Perform the Gram-Schmidt process on the following sequence of vectors. -3 -2 6 -3 6 y= -5 х — 3 -4 3 1 2 -2...
5. (12 pts) Let A= 4 -1 2 -1 3 -3 2 0 2 1 Find A-? using the formula A-1 adj(A). det(A)
Let A1 1 and b = {12, 6, 18)T (a) Use the Gram-Schmidt process to find an orthonormal basis for the column basis for the column space of A; (b) Factor A into a product QR, where Q has an orthonormal set of column vectors and R is upper triangular; (c) Solve the least squares problem Ax = b. Use the results from problem! (c) to find the least square solution of Ax = b
please answer correctly. i will not rate if it’s not correct and includes steps. Thank you. ex..2 3 4-6 -8 0 -1 31 Find a besis for the image of T and a basis for the kornel of T. (Thse bases sed not be orthonormal) 2. (10 points) Let V be the linear subspace of R consisting of all vectors that satisty z Here, z, denotes the ith componest of a vector E.) 3r2 and (a) What is the dimension...
Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W! Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W!
1. Find a basis for the image and kernel of the following matrices. It does not have to be an orthonormal basis, but don't include more vectors than needed. (1 1 1\ (a) A= (1 2 3 11 3 5) 12 2 21 (b) A = 2 2 2 12 2 2) 11 11 (c) A= 1 3 11 -1) NNN
Problem 1 Let A= 3 2 13 1 5 7 11 8 -3 9 10 -6 -4 12 8 a) [4 pts) Find a basis for N(A) in rational format. b) (3 pts) Find a particular solution to the matrix equation A*x= 5 -2 14 c) [3 pts] Use your answers in a), b) and the Superposition Principle to express the general solution in vector form to the matrix equation in b).